The irony of large numbers

Like me (here), Andrew (link) shudders when journalists use the term "law of large numbers". Statisticians use the law to mean some very specific but it seems that in the business community, it means something like "diminishing returns to scale".

It's worse than that. When statisticians use the term "law of large numbers", it is always to refer to "small numbers"! The political poll is a great example of the law of large numbers at work; it always amuses my students that a poll of a few thousand people in the U.S. enables us to make general statements about hundreds of millions of people. Notice that the law of large numbers is invoked to support a sample of apparently small size.